Math Problem Statement

Which is a y-intercept of the continuous function in the table?

Solution

The question asks for the y-intercept of the continuous function shown in the table. The y-intercept is the point where the function crosses the y-axis, which means the value of x=0x = 0.

From the table, when x=0x = 0, f(x)=6f(x) = -6. Therefore, the y-intercept is at the point (0,6)(0, -6).

The correct answer is:

  • (0,6)(0, -6)

Would you like further details or have any questions?

Here are 5 related questions to explore further:

  1. What does the x-intercept represent in a function?
  2. How can you find the slope between two points from a table like this one?
  3. What is the significance of the continuity of a function?
  4. How can a function's behavior be predicted from its table of values?
  5. What are the different types of intercepts a function can have?

Tip: The y-intercept is always found where x=0x = 0, while the x-intercept(s) occur where f(x)=0f(x) = 0.

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Intercepts

Formulas

y-intercept occurs at x = 0

Theorems

Continuity of functions

Suitable Grade Level

Grades 7-9